# SDFlow: Similarity-Driven Flow Matching for Time Series Generation

arXiv: https://arxiv.org/abs/2605.05736 · HTML: https://mlsanity.com/paper/2605.05736/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 27 of its 34 references that are in the map.
- First posted on arXiv 7 May 2026.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 27 of 27)

- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Zero-Shot Text-to-Image Generation](https://mlsanity.com/paper/2102.12092/) (2021)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Taming Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2012.09841/) (2020)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [MaskGIT: Masked Generative Image Transformer](https://mlsanity.com/paper/2202.04200/) (2022)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [Scheduled Sampling for Sequence Prediction with Recurrent Neural Networks](https://mlsanity.com/paper/1506.03099/) (2015)
- [T2M-GPT: Generating Human Motion from Textual Descriptions with Discrete Representations](https://mlsanity.com/paper/2301.06052/) (2023)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [Time Series Forecasting With Deep Learning: A Survey](https://mlsanity.com/paper/2004.13408/) (2020)
- [Flow Matching on General Geometries](https://mlsanity.com/paper/2302.03660/) (2023)
- [Diffusion-based Time Series Imputation and Forecasting with Structured State Space Models](https://mlsanity.com/paper/2208.09399/) (2022)
- [How Faithful is your Synthetic Data? Sample-level Metrics for Evaluating and Auditing Generative Models](https://mlsanity.com/paper/2102.08921/) (2021)
- [Diffusion-TS: Interpretable Diffusion for General Time Series Generation](https://mlsanity.com/paper/2403.01742/) (2024)
- [TimeVAE: A Variational Auto-Encoder for Multivariate Time Series Generation](https://mlsanity.com/paper/2111.08095/) (2021)
- [Generalization in Generation: A closer look at Exposure Bias](https://mlsanity.com/paper/1910.00292/) (2019)
- [Variational Flow Matching for Graph Generation](https://mlsanity.com/paper/2406.04843/) (2024)
- [COT-GAN: Generating Sequential Data via Causal Optimal Transport](https://mlsanity.com/paper/2006.08571/) (2020)
- [On the Constrained Time-Series Generation Problem](https://mlsanity.com/paper/2307.01717/) (2023)
- [FlowTS: Time Series Generation via Rectified Flow](https://mlsanity.com/paper/2411.07506/) (2024)
- [Purrception: Variational Flow Matching for Vector-Quantized Image Generation](https://mlsanity.com/paper/2510.01478/) (2025)
- [TimeMar: Multi-Scale Autoregressive Modeling for Unconditional Time Series Generation](https://mlsanity.com/paper/2601.11184/) (2026)

## Built on by (most cited first, 3 of 3)

- [Evaluating Generative Time-Series Models on Data with Point Masses](https://mlsanity.com/paper/2608.09692/) (2026)
- [HALO: Enhancing Time Series Generation via Hyperspherical Latents and Masked AutoregRessive Modeling](https://mlsanity.com/paper/2609.34511/) (2026)
- [ProtoFlow: Prototype-Guided Flow Matching for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2610.01320/) (2026)

## Abstract (arXiv)

Vector quantization (VQ) with autoregressive (AR) token modeling is a widely adopted and highly competitive paradigm for time-series generation. However, such models are fundamentally limited by exposure bias: during inference, errors can accumulate across sequential predictions, leading to pronounced quality degradation in long-horizon generation. To address this, we propose SDFlow (Similarity-Driven Flow Matching), a non-autoregressive framework that operates entirely in the frozen VQ latent space and enables parallel sequence generation via flow matching. We tackle three key challenges in making this transition: (1) eliminating exposure bias by replacing step-wise token prediction with a global transport map; (2) mitigating the high-dimensionality of VQ token spaces via a low-rank manifold decomposition with a learned anchor prior over the latent manifold; and (3) incorporating discrete supervision into continuous transport dynamics by introducing a categorical posterior over codebook indices within a variational flow-matching formulation. Extensive experiments show that SDFlow achieves state-of-the-art performance, improving Discriminative Score and substantially reducing Context-FID, particularly for challenging long-sequence generation. Moreover, SDFlow provides significant inference speedups over autoregressive baselines, offering both high fidelity and computational efficiency. Code is available at https://github.com/William-Liwei/SDFlow